Rewrite as a simplified fraction. ${3.23\overline{5} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3235.5555...\\ 100x &= 323.5555...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2912}$ ${x = \dfrac{2912}{900}} $ ${x = \dfrac{728}{225}} \text{or} {3 \dfrac{53}{225}}$